IMPROVED ERROR ESTIMATION FOR THE PARTIALLY PENALIZED IMMERSED FINITE ELEMENT METHODS FOR ELLIPTIC INTERFACE PROBLEMS.

This paper is for proving that the partially penalized immersed finite element (PPIFE) methods developed in [25] converge optimally under the standard piecewise H² regularity assump-tion for the exact solution. In energy norms, the error estimates given in this paper are better than those in [25] where a stronger piecewise H³ regularity was assumed. Furthermore, with the standard piecewise H² regularity assumption, this paper proves that these PPIFE methods also converge optimally in the L² norm which could not be proved in [25] because of the excessive H³ regularity requirement. [ABSTRACT FROM AUTHOR]